Question: What's the first wrong statement in the proof below that $ \triangle EBC \cong \triangle ABC$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle ACB \cong \angle BDE$ $, \ $ $ \overline{BC} \cong \overline{BD}$ $, \ $ $ \angle ABC \cong \angle DBE$ $, \ $ $ \angle ACB \cong \angle ECF$ $, \ $ $ \overline{BC} \cong \overline{CF}$ $, \ $ and $\ $ $ \angle ABC \cong \angle CFE$ Proof $ \triangle EBD \cong \triangle ABC$ because ASA $ \overline{BE} \cong \overline{AB}$ because corresponding parts of congruent triangles are congruent $ \overline{BD} \cong \overline{AC}$ because corresponding parts of congruent triangles are congruent $ \angle BED \cong \angle CBE$ because alternate interior angles are equal $ \triangle ABC \cong \triangle EFC$ because ASA $ \triangle EBC \cong \triangle ABC$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \overline{AC} \cong \overline{BD}$ is the first wrong statement.